This paper proposes a general method of extending the effective invisible regions for both the shell-like interior cloak and the complementary media exterior cloak, without affecting their original cloaking regions. The proposed method is based on layered spatial mapping instead of the intact mapping. Certain interior or exterior invisible regions can be obtained by properly using a compressed or folded transformation in each space layer. Therefore, the proposal enables the as-designed cloaks to provide multiple invisible regions of different types simultaneously. Thus objects can be hidden in the interior cavity and/or in the exterior space, or even be embedded between the cloaking shells.

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